Canonical State-Space Realization of 3-D Separable Denominator Discrete Systems

In this paper, the state-space realization of 3-D discrete systems having transfer functions with separable denominators is considered. The proposed state-space model has a canonical form and can be derived directly from the transfer function coefficients. Using the fact that the denominator is separable, the dimensionality of the proposed model is lower than that in the non-separable case. In addition, block diagrams for the transfer function are proposed. The proposed realization is useful for the implementation of these systems. Three examples are presented to illustrate the results of the paper.